🧮 algebra

1. **State the problem:** Factor the expression $$x^2 - 9y^2$$.

1. **Stating the problem:** Simplify the expression $$91 - 92 \times 89 - 90$$. 2. **Formula and rules:** According to the order of operations (PEMDAS/BODMAS), multiplication must

1. **Nyatakan masalah:** Kita diminta untuk memfaktorkan ekspresi $$3xy^2 - 6x^2y$$. 2. **Formula dan aturan penting:** Pemfaktoran adalah proses mengubah ekspresi menjadi hasil ka

1. Diketahui fungsi $f(x) = 3x + 5$ dan $g(x) = 7x - 4$. Kita diminta menentukan komposisi fungsi dan inversnya. 2. a. Menentukan $(f \circ g)(x)$ atau $f(g(x))$:

1. **State the problem:** We are given a map scale where $\frac{1}{2}$ inch represents 8 miles. We need to find the actual distance between two points that are $1\frac{1}{4}$ inche

1. The problem is to solve all questions from NCERT Class 8 Chapter 8.3. 2. Since the user requested all question solutions, we will solve the first question completely as per inst

1. The problem is to understand the meaning and use of the square root symbol $\sqrt{ }$. 2. The square root symbol $\sqrt{ }$ represents the principal square root of a number, whi

1. **State the problem:** We need to expand the expression $(7n+8)(2m-5)$ and then simplify the expression $\frac{5}{7}m - \frac{1}{3}(5 - 9n)$ as a single fraction.

1. **Problem 4:** Find the length of one side of a square courtyard whose area is given by $x^2 + 10x + 25$.\n\n2. The formula for factoring perfect square trinomials is:\n$$a^2 +

1. **Problem:** A rectangular park has an area represented by $$15x^3 - 20x^2$$. We need to find its dimensions by factoring the expression. 2. **Formula and rules:** To factor a p

1. **State the problem:** Simplify the expression $$\frac{3}{7b}(14a - 21b) - \frac{a}{2b}$$ and match it to one of the given options. 2. **Recall the distributive property:** $$k(

1. **State the problem:** Solve the equation $$\frac{1}{x+4} - \frac{1}{x-7} = \frac{11}{30}$$ using the quadratic equation method. 2. **Find a common denominator and combine the f

1. **State the problem:** We need to solve the quadratic equation $$18abx^2 + (5a^2 - 7b^2)x - 9ab = 0$$ for $x$ using the quadratic formula.

1. **State the problem:** Solve the quadratic equation $$12abx^2 - \left(9a^2 - 8b^2\right)x - 6ab = 0$$ for $x$ using the quadratic formula. 2. **Recall the quadratic formula:** F

1. **Problem Statement:** Identify which graphs represent pairs of inverse functions. 2. **Key Concept:** Two functions $f$ and $g$ are inverses if and only if their graphs are sym

1. **State the problem:** We need to find the value of $n$ when $n$ arithmetic means are inserted between $a$ and $100$, the ratio of the first mean to the last mean is $1:7$, and

1. The problem is to add the fractions $\frac{1}{2}$ and $\frac{2}{4}$.\n\n2. To add fractions, they must have a common denominator. The denominators here are 2 and 4.\n\n3. The le

1. **State the problem:** Solve for $x$ in the equation:

1. **State the problem:** Simplify the expression $$\frac{2 - \frac{3}{5}}{1 \frac{3}{10} + 5}$$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Simplify the expression $$\frac{3.2 - \frac{3}{5}}{1 \frac{3}{10} + 5}$$. 2. **Convert mixed numbers and decimals to improper fractions:**

1. **Problem 1: Minimum number of bread loaves for packing** The baker can pack bread in boxes of $15$ or $20$ loaves. We want to find the minimum number of bread loaves that can b